Show the detailed solution! And the final result of question c!

Problem 4. Data Distribution (20 points) Table 3 shows 2, 100 student grades and their preferences on courses collected from 10 years of a university's data. (a) (6 points) Let p=[pApBpCpDpF]T be the probability distribution of the course grade. Find p. (b) (4 points) Assuming the course grade and student's preference on courses are independent, what is the expected number of students who both select CS412 and gets A? 3 Table 3: Student grades and their preference on courses. (c) (10 points) Calculate the 2 correlation value for "CS412" and "CS512